Kernel Density Estimation from Record-Breaking Data

In some experiments, only values smaller than all previous ones are observed, such as destructive stress testing and industrial quality control experiments. Here, for such record-breaking data, kernel density estimation is considered. For a single record-breaking sample, consistent estimation is not possible except in the extreme tails of the distribution. Hence, replication is required, and for m such independent record-breaking samples, the kernel density estimator is shown to be strongly consistent and asymptotically normal as m → ∞. Also, some computer simulation results and examples are presented.